Papers › A Quantum Algorithm for Solving Linear Differential Equations: Theory and Experiment
A Quantum Algorithm for Solving Linear Differential Equations: Theory and Experiment
Tao Xin, Shijie Wei, Jianlian Cui, Junxiang Xiao, Iñigo Arrazola, Lucas Lamata, Xiangyu Kong, Dawei Lu, Enrique Solano, Guilu Long
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We present and experimentally realize a quantum algorithm for efficiently solving the following problem: given an N×N matrix ℳ, an N-dimensional vector b, and an initial vector x(0), obtain a target vector x(t) as a function of time t according to the constraint dx(t)/dt=ℳx(t)+b. We show that our algorithm exhibits an exponential speedup over its classical counterpart in certain circumstances. In addition, we demonstrate our quantum algorithm for a 4×4 linear differential equation using a 4-qubit nuclear magnetic resonance quantum information processor. Our algorithm provides a key technique for solving many important problems which rely on the solutions to linear differential equations.
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